1. Field of the Invention
The present invention relates to an apparatus and method of adaptive frequency offset estimations for a receiver, and particularly to an apparatus and method of adaptive frequency offset estimations for a receiver based on DBPSK demodulations.
2. Description of the Related Art
The carrier frequency offset can be determined directly by estimating a rotation rate of the phase offset between two adjacent samples. A digital frequency offset estimator is commonly used to extract phase increments between consecutive symbols. Since the transmitted data message is modulated in received symbols, the modulated data effect should be eliminated before the phase offset being calculated. A broadly used powering approach for DBPSK in the prior art is shown as follows.
FIG. 1 shows a block diagram of an apparatus in a conventional demodulator that estimates the phase offset of input symbols based on a DBPSK modulation approach. As shown in FIG. 1, the apparatus in a conventional demodulator includes a phase-increment extraction circuit 40, a squaring circuit 25, a summation circuit 20, an argument circuit 30, and a divider 35, while the phase-increment extraction circuit 40 further includes a delay circuit 41, a conjugate circuit 42, and a multiplier 45. The phase extraction circuit 40 receives input symbols represented by Zk=dkejkΔθ and the delay circuit 41 is used to store the last input symbol Zk−1. The conjugate circuit 42 generates a conjugate Zk−1* of the last input symbol Zk−1 and the multiplier 45 derives a product of the input symbol Zk and the conjugate Zk−1* of the last input symbol Zk−1 to generate a phasor Rk. The phasor Rk has an argument containing the phase increment Δθ rotated according to frequency offsets and the phase difference of successive samples of the modulation. The squaring circuit 25 receives the phasor Rk and generates a square phasor Rk2, which is insensitive to the phase difference of successive samples based on the DBPSK modulation. The summation circuit 20 calculates the summation of the square phasors ΣRk2 by summing up all the previous squares phasors, and finally the argument circuit 30 extracts the phase offset of the summation ΣRk2 rotated by the frequency offset. The phase offset of the summation of the squares phasors ΣRk2, similar to the expectation of the phase offsets of the squares Rk2, is equal to double phase offset of the phasor Rk, 2ΔfT. The divider 35 divides the double phase offset 2ΔfT to yield the phase offset ΔfT of the phasor Rk, therefore the frequency offset f can be estimated by using the phase offset of the phasor Rk.
As well known by the skills in the art, the squaring operations will reduce so-called SNR (Signal-to-Noise Ratio) in the conventional approach. AssumesRk=signal+noiseandRk2=signal2+2×signal×noise+noise2
Basically, a signal is significant larger than noise (i.e. |signal|>>|noise|), so the term noise2 can be ignored in comparison with the other two. Therefore, the square Rk2 can be approximated as:Rk2≈signal2+2×signal×noiseand the SNR after the squaring operation is:
            signal      2        ÷          (              2        ×        signal        ×        noise            )        =            1      2        ×          (              signal        ÷        noise            )      which is obvious a half of the SNR of the phasor Rk.
Obviously, there are disadvantages in the conventional frequency estimation approach as follows. Firstly, noise will be enhanced in the squaring circuit as aforementioned, which significantly reduces SNR and thus degrades the performance for obtaining decision boundaries while the training sequence is employed. In other word, the conventional approach is a time-cost way to make estimations achieve application requirement. However, for those applications that are not suffered by time-cost so seriously when the training sequence scheme is employed, the estimated phase offsets may not achieve accuracy requirements of these applications. Secondly, the conventional approach requires quite a complicated circuit for implementations. For example, the squaring circuit basically requires four multipliers to calculate the squaring values, and there requires a divider, which is usually composed of complicated circuitry for calculating the estimated phase offsets. There is a need to provide an apparatus and method that estimates frequency offsets adapted to a data decision approach with simpler circuit configurations and higher SNR than the conventional approach.